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Introduction to Functional Programming
Introduction to Functional Programming

... lambda calculus. It is widely agreed that languages such as Haskell and Miranda are purely functional, while SML and Scheme are not. However, there are some small differences of opinion about the precise technical motivation for this distinction. Scheme and Standard ML are predominantly functional ...
Functional Programming in Haskell
Functional Programming in Haskell

... Functional vs. Imperative Programming Imperative programming: The program specifies what the computer should do. Functional programming: The program specifies what the value of a function should be. The exact sequence of steps to compute this value is left unspecified. This is one form of declarati ...
Another problem to solve…
Another problem to solve…

... F(n) = n * F(n-1) for n > 0 F(0) = 1 Base case ...
def fac(n)
def fac(n)

... F(n) = n * F(n-1) for n > 0 F(0) = 1 Base case ...
Lazy evaluation - Computer Science and Engineering
Lazy evaluation - Computer Science and Engineering

... request for some output from another function requiring some input. • Therefore, the functions call each other and returns values as and when required. • For example, in tree equality, if first value of both the trees in preorder sequence are equal then second element of first tree is computed follo ...
Functional Programming in Scheme
Functional Programming in Scheme

... dynamically typed language or, equivalently, latent typed. In a latent typed language, types are associated to values rather than to the program identifiers and the type checking is performed at run time. Also Scheme is sometimes considered as a weak-typed language since values of any type can be mi ...
document
document

... letrec in Scheme • letrec – all the bindings are in effect while their initial values are being computed, allows mutually recursive definitions (letrec ((even? (lambda (n) (if (zero? n) #t (odd? (- n 1))))) (odd? (lambda (n) (if (zero? n) #f (even? (- n 1)))))) (even? 88)) ...
COS220lec52_FP
COS220lec52_FP

... Introduction to FP Imperative programming vs. functional programming Language applied to functional programming is LISP – LISt Programming. It was invented to provide language features for list processing, the need for which grew out of the first application in the area of AI, expert systems, knowl ...
C# is a functional programming language
C# is a functional programming language

... The CLR has direct support for many of the features described here ◦ Delegates are special classes with fast calling convention ◦ Generics (parametric polymorphism) is implemented by just-intime specialization so no boxing is required ◦ Closure conversion is done by the C# compiler, which shares env ...
ppt - Dave Reed
ppt - Dave Reed

...  each call to add keeps the vector sorted  each call to addFast is O(1), but means the vector may not be sorted  IsStored first checks the data field: if !isSorted, then call MergeSort first ...
Closure and Environment
Closure and Environment

... Nested HOL is a key feature in modern functional programming languages And now has grown into other language ...
Pretty Printing with Lazy Dequeues
Pretty Printing with Lazy Dequeues

... For our first implementation of the token interpreter we do not yet care about boundedness. So the interpreter decides if a group is formatted horizontally or vertically only after it has been traversed, that is, the decision is made at the Close token of the group. An implementation that makes the ...
X - Rensselaer Polytechnic Institute: Computer Science
X - Rensselaer Polytechnic Institute: Computer Science

... • Embedding is when procedure values are put in data structures • Embedding has many uses: – Modules: a module is a record that groups together a set of related operations – Software components: a software component is a generic function that takes a set of modules as its arguments and returns a new ...
Appendix B
Appendix B

... nonlocal references are resolved at the point of function definition. Static scoping is implemented by associating a closure (instruction pointer and environment pointer) with each function as it is defined. The run-time execution stack maintains static links for nonlocal references. Top-level defin ...
Class Notes 2b: Scheme Reference
Class Notes 2b: Scheme Reference

... • It correctly treats functional arguments, thanks to lexical scoping. – Functions are first-class objects: they can be created, assigned to variables, passed as arguments, returned as values. ...
CS-Intro-AI-LISP - Geometric and Intelligent Computing Laboratory
CS-Intro-AI-LISP - Geometric and Intelligent Computing Laboratory

... Under the hood… • Lisp doesn't need type declaration because everything is a pointer (i.e., the values of symbols have types associated w/ them; atoms, lists, integers, etc.) ...
Drexel-CS-Intro-AI-LISP
Drexel-CS-Intro-AI-LISP

... • In reality, both pointers to A point to the SAME symbol (i.e., the same exact mem location) • EQ: tests for memory location exactly, therefore, atoms only! • LISP automatically makes sure that all refs to some symbol actually point to the UNIQUE point in mem that the symbol happens to be stored ph ...
Calculating Functional Programs - Research School of Computer
Calculating Functional Programs - Research School of Computer

... 5. Calculating Functional Programs ...
19. Introduction to evaluation order
19. Introduction to evaluation order

... Different evaluation orders give different 'results' • The number 1 • A non-terminating calculation Two different semantics of function application are involved: • Strict: A function call is well-defined if and only if all actual parameters are well-defined • Non-strict: A function call can be well- ...
Foundations of Functional Programming
Foundations of Functional Programming

... 5. Its notions of confluence (Church-Rosser property), termination, and normal form apply generally in rewriting theory. 6. Lisp, one of the first major programming languages, was inspired by the λ-calculus. Many functional languages, such as ML, consist of little more than the λ-calculus with addit ...
Downloadable PowerPoint file
Downloadable PowerPoint file

... efficient as iteration  This is always possible in the face of tail recursion, where the recursive call is the last operation before returning ...
Cryptography - Mathematical Association
Cryptography - Mathematical Association

... There are a few things to note about this definition.  If the value of a is 0 or b2 – 4ac < 0 then an error is raised. The appropriate error comment will be printed on screen.  otherwise is used to catch any values that do not satisfy any of the other clauses – we could have used this in the last ...
Lambda Calculus as a Programming Language
Lambda Calculus as a Programming Language

... "theoretically" we should. We forbid the use of the symbol as a free variable within the λexpression itself. This is in line with Lambda calculus where λ-expressions must be textually finite and where free variables have nothing to do with defining recursive functions. The notation E1 = E2 is used t ...
nil
nil

... Definition From the "comp.lang.functional FAQ" Functional programming is a style of programming that emphasizes the evaluation of expressions, rather than execution of commands. The expressions in these language are formed by using functions to combine basic values. A functional language is a langua ...
fp_in_scheme
fp_in_scheme

... of the results of applying the function to elements taken from each list > (map abs '(3 -4 2 -5 -6)) ...
1 2 3 4 5 ... 9 >

Tail call

In computer science, a tail call is a subroutine call performed as the final action of a procedure. If a tail call might lead to the same subroutine being called again later in the call chain, the subroutine is said to be tail-recursive, which is a special case of recursion. Tail recursion (or tail-end recursion) is particularly useful, and often easy to handle in implementations.Tail calls can be implemented without adding a new stack frame to the call stack. Most of the frame of the current procedure is not needed any more, and it can be replaced by the frame of the tail call, modified as appropriate (similar to overlay for processes, but for function calls). The program can then jump to the called subroutine. Producing such code instead of a standard call sequence is called tail call elimination. Tail call elimination allows procedure calls in tail position to be implemented as efficiently as goto statements, thus allowing efficient structured programming. In the words of Guy L. Steele, ""in general procedure calls may be usefully thought of as GOTO statements which also pass parameters, and can be uniformly coded as [machine code] JUMP instructions.""Traditionally, tail call elimination is optional. However, in functional programming languages, tail call elimination is often guaranteed by the language standard, and this guarantee allows using recursion, in particular tail recursion, in place of loops. In such cases, it is not correct (though it may be customary) to refer to it as an optimization. The special case of tail recursive calls, when a function calls itself, may be more amenable to call elimination than general tail calls.
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